RhBi$_{4}$ Structure: A4B_cI120_230_h_c-001
| Prototype | Bi$_{4}$Rh |
| AFLOW prototype label | A4B_cI120_230_h_c-001 |
| ICSD | 58854 |
| Pearson symbol | cI120 |
| Space group number | 230 |
| Space group symbol | $Ia\overline{3}d$ |
| AFLOW prototype command |
aflow --proto=A4B_cI120_230_h_c-001
--params=$a, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}$ |
- (Glagoleva, 1956) give three slightly different values for the location of the bismuth atoms. We choose their final set of coordinates. The ICSD entry is from the earlier publication (Zhdanov, 1954).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24c) | Rh I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24c) | Rh I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}$ | (24c) | Rh I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24c) | Rh I |
| $\mathbf{B_{5}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (24c) | Rh I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- \frac{1}{8}a \,\mathbf{\hat{z}}$ | (24c) | Rh I |
| $\mathbf{B_{7}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24c) | Rh I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24c) | Rh I |
| $\mathbf{B_{9}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24c) | Rh I |
| $\mathbf{B_{10}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}$ | (24c) | Rh I |
| $\mathbf{B_{11}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (24c) | Rh I |
| $\mathbf{B_{12}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (24c) | Rh I |
| $\mathbf{B_{13}}$ | = | $\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{14}}$ | = | $\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{15}}$ | = | $\left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{16}}$ | = | $- \left(y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}- a \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{17}}$ | = | $\left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{18}}$ | = | $- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{19}}$ | = | $\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{20}}$ | = | $\left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}- \left(y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{21}}$ | = | $\left(x_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{22}}$ | = | $- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{23}}$ | = | $- \left(x_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{24}}$ | = | $\left(x_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}- \left(y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}- a \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{25}}$ | = | $\left(x_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{26}}$ | = | $- \left(x_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{27}}$ | = | $- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{28}}$ | = | $\left(x_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{29}}$ | = | $\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{30}}$ | = | $\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{31}}$ | = | $- \left(y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{32}}$ | = | $\left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{33}}$ | = | $\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{34}}$ | = | $\left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{35}}$ | = | $\left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{36}}$ | = | $- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{37}}$ | = | $- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{38}}$ | = | $\left(y_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{39}}$ | = | $- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{40}}$ | = | $\left(y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+a \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{41}}$ | = | $- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{42}}$ | = | $\left(x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{43}}$ | = | $\left(x_{2} - y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{44}}$ | = | $- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{45}}$ | = | $- \left(x_{2} + z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{2}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{46}}$ | = | $\left(x_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{47}}$ | = | $\left(x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{48}}$ | = | $\left(- x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}+a \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{49}}$ | = | $\left(- x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{50}}$ | = | $\left(x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{51}}$ | = | $\left(x_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{52}}$ | = | $- \left(x_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(y_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{53}}$ | = | $\left(y_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{54}}$ | = | $- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{55}}$ | = | $\left(y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{56}}$ | = | $- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{2}+\left(- x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{57}}$ | = | $\left(x_{2} - y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{58}}$ | = | $- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{59}}$ | = | $- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
| $\mathbf{B_{60}}$ | = | $\left(x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96h) | Bi I |
References
- V. P. Glagoleva and G. S. Zhdanov, The Structure of Superconductors. IX. Roentgenographic Determination of the Structure of α-Bi$_{4}$Rh, Soviet Phys.–-JETP 3, 155–158 (1956).
- G. S. Zhdanov, The binary systems Bi - Ni and Bi - Rh, Trudy Inst. Geol. Nauk Akad. Nauk S.S.S.R. 10, 99–116 (1954).
Found in
- P. Villars, H. Okamoto, and K. Cenzual, eds., ASM Alloy Phase Diagram Database (ASM International, 2018), chap. Bismuth-Rhodium Binary Phase Diagram (1962 Ross R.G.). Copyright © 2006-2018 ASM International.
Prototype Generator
aflow --proto=A4B_cI120_230_h_c --params=$a,x_{2},y_{2},z_{2}$